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Accurate acquisition of the complex refractive index of materials is of great significance to understand their physical properties. Based on a single time-domain transmission model in $Y$ -band, here, we develop a free-space nondestructive testing method combined with parameter extraction of flat plate materials. This method overcomes the limitation of the narrow frequency band of S-parameters of vector network analyzer (VNA), truncates multiple echo interferences in time-domain signals inside sample after the inverse fast Fourier transform (IFFT), and eliminates the crimping effect of the calculation results. In order to ensure the good signal integrity of the model, an empirical formula is proposed to calculate the minimum thickness of the sample corresponding to unit bandwidth. An $8f$ quasi-optical system is designed and optimized to provide a measuring condition of terahertz (THz) plane wave with high energy density. Compared with the values calculated by the conventional methods, the refractive index deviation is less than 0.004 (0.2%), which verifies the effectiveness and applicability of our proposed method. The adaptability of different processes to the corresponding physical transmission model is further analyzed, and the reasons for the calculation deviation are explained. This work reduces the complexity and difficulty of the material measurement in the $Y$ -band, as well as the requirements of system calibration. [ABSTRACT FROM AUTHOR]